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Mikael Pichot

Publications and source records attributed to Mikael Pichot.

At least 19 recordsLinked to original sources
arXiv2021

Surgery on discrete groups

We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.

math.GR↗
arXiv2021

Surgery on Aut(F2)

We study a geometric construction of certain finite index subgroups of Aut(F2).

math.GR↗
arXiv2020

Pauli matrices and ring puzzles

We study a family of tessellations of the Euclidean plane which are obtained by local developments of algebraic equations satisfied by the Pauli matrices.

math.GR↗
arXiv2018

Isomorphisms and parity of complexes of rank 7/4

We study the isomorphism types of simply connected complexes of rank 7/4 using a local invariant called the parity. We show that the parity can be computed explicitly in certain constructions arising from surgery.

math.GR↗
arXiv2017

Random group cobordisms of rank 7/4

We construct a model of random groups of rank 7/4, and show that in this model the random group has the exponential mesoscopic rank property.

math.GR↗
arXiv2014

Aut(F2) puzzles

This paper studies Aut(F2) and groups closely related to it from a geometric perspective.

math.GR↗
arXiv2014

Random groups and nonarchimedean lattices

We consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to M. Gromov's well-known constructions and include for example a "density model" for groups of intermediate rank. The main novelty is the higher rank nature of the random groups. They are randomization of certain families of lattices in algebraic groups (of rank 2) over local fields.

math.GR↗
arXiv2013

A free product formula for the sofic dimension

It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$ satisfies the equality \[ s(G)=\h(G_1^0)s(G_1)+\h(G_2^0)s(G_2)-\h(G_3^0)s(G_3) \] where $\h$ is the normalized Haar measure on $G$.

math.DS↗
arXiv2012

Intermediate rank and property RD

We introduce concepts of intermediate rank for countable groups that "interpolate" between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are especially interested in interpolation between rank 1 and rank 2. For instance, we construct groups "of rank 7/4". Our setting is essentially that of non positively curved spaces, where concepts of intermediate rank include polynomial rank, local rank, and mesoscopic rank. The resulting framework has interesting connections to operator algebras. We prove property RD in many cases where intermediate rank occurs. This gives a new family of groups satisfying the Baum-Connes conjecture. We prove that the reduced $C^*$-algebras of groups of rank 7/4 have stable rank 1.

math.MG↗
arXiv2012

Sofic dimension for discrete measured groupoids

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.

math.DS↗
arXiv2011

Orbit equivalence and sofic approximation

Given an ergodic probability measure preserving dynamical system $\G\acts (X,μ)$, where $\G$ is a finitely generated countable group, we show that the asymptotic growth of the number of finite models for the dynamics, in the sense of sofic approximations, is an invariant of orbit equivalence. We then prove an additivity formula for free products with amenable (possibly trivial) amalgamation. In particular, we obtain purely combinatorial proofs of several results in orbit equivalence theory.

math.DS↗
arXiv2009

Le coût est un invariant isopérimétrique

For a type II_1 ergodic measured equivalence relation R on a probability space without atom, we prove that h(R)=2C(R)-2, where C(R) is the cost, and h(R) the isoperimetric constant. This follows recent result by Lyons and the authors.

math.OA↗